probing the nuclear eos with fragment production
DESCRIPTION
Probing the nuclear EOS with fragment production. Maria Colonna Laboratori Nazionali del Sud (Catania ). Fragmentation events: IMF properties in central and semi - peripheral collisions (neutron-rich systems) Kinematical properties Size and asymmetry (N/Z) - PowerPoint PPT PresentationTRANSCRIPT
Probing the nuclear EOS with fragment production
Maria Colonna Laboratori Nazionali del Sud (Catania)
Fragmentation events: IMF properties in central and semi-peripheral collisions (neutron-rich systems)• Kinematical properties• Size and asymmetry (N/Z)Insight into the reaction mechanism responsible forfragment emission and isospin transport: density vs N/Z concentration gradients Dependence of the results on the asy – EOS
A new method to incorporate full fluctuations into a transport treatment (Boltzmann-Langevin theory)
Conclusions and perspectives
( , , ) ( , , ) ( , , ) ( ) ( )K r p t K r p t p p r r r t t
Instantaneous equilibrium
)1()(2 ffpf
),()()(),( cov2 ppppppp f
fWWfdt
df
Ensemble average
Langevin: randomwalk in phase-space
Semi-classical approach to the many-body problem
Time evolution of the one-body distribution function ( , , )f r p t
Boltzmann
),,()(),(),(),( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfh
i
i
Vlasov: mean field
Boltzmann: average collision term
( ) ( ) NNf i f i
dp p E E
d
3 3 32 1 2
2 1' 2'3 3 3( , ) (12 1 2 )
d p d p d pW r p f f f w
h h h Loss term
Correlation function
)( WW
dt
d
Focus on the variance σ2f = <δfδf>
D(p,p’,r)
Stochastic mean field (SMF) calculations
b = 4 fm b = 6 fm
Sn124 + Sn124, E/A = 50 MeV/A
Chomaz,Colonna, Randrup Phys. Rep. 389 (2004)
Central collisions
Ni + Au, E/A = 45 MeV/A
(fluctuations projected on ordinary space)
Isospin Transport and Chemical Potentials
I
EIEjj sym
sympn
)()(
IDDj
IDDjIppp
Innn
currents
diffusion
Diffusion Drift
drift
pnqI
D
D
T
qIq
TI
,,
,
Direct Access to Value and Slope of the Symmetry Energy at ρ !
asy-soft
asy-stiff
E/A (ρ) = Es(ρ) + Esym(ρ)I²I=(N-Z)/A
IMF properties in central collisions
Sn124 + Sn124, E/A = 50 MeV/A, b = 2 fm
• bubble-like configuration• radial flow• correlations:Size, N/Z vsradial distance - velocity
Primary fragment propertiesX.T.Liu et al, PRC69(2004) V.Baran et al, NPA703(2002)
N/Z vs charge
1200 events for each reaction
Proton/neutron repulsion:larger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems (Δ’>Δ)
N/Z vs fragment energy (1) Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm
“gas” phase(pre-equilibrium)
asy-stiff asy-soft
“liquid”
asy-stiff asy-soft
N = Σi Ni , Z = Σi Zi 1.64
Double ratio = (N/Z)2/(N/Z)1
Δ
Δ’
3≤ Zi ≤ 10
N/Z vs fragment energy (2)
To combine the two effects:Different slope vs. n-rich cluster emission “shifted” N/Z: N/Zs = N/Z – N/Z(E=0)Larger sensitivity to the asy-EoSis observed in the double N/Zs ratio
IMF emission
Double ratio R = (N/Z)2/(N/Z)1
Large double ratio in the asy-stiff case !(opposite to pre-equ. emission)
Famiano et al. PRL 06
Pre-equilibrium emission
IMF emission
asy-stiff
asy-soft
3≤ Zi ≤ 10
Sn124 – Sn112
(BUU calculations)
Δ
Δ’
Still arbitrary:•r-space distance
Procedure easily applicable to nuclear reactions Careful check of Pauli-blockingTake into account possible nucleon deformations
in p space
I J
J’
I’
p-space
Our improved method
• test particles i and j cells I and J
•
• Spherical search around I and J
•“clouds” rotated to final states
),,,min(, JIJItransCM nnnnndrr
x Pauli violations: average trajectory altered
x Shape of more similar to classical than to quantum case
)(2 pf
Fluctuations in phase space
Original procedure by Bauer et al.
• Cross section reduction
1 nucleon = NTEST nearest neighbours
• Phase-space distance
• < pi > and < pj > ; Δp assigned to each “cloud”
•Clouds translated to final states ( no rotation)
• Pauli blocking checked only for i and j t.p.
-Δp
Δp
TEST
NNNN N
2222 )()/()( kiFkiik rrRpppd
Bauer, Bertsch, Das Gupta, PRL58 (1987) 58
(Improve the treatment of fluctuations in p space)
r-space: periodic 3-D box, l = 26 fm;
ρ = 0.16 fm-3 (2820 nucleons); 500 test particles
p-space: Fermi-Dirac configuration , kT = 5 MeV
Illustrative results
t =0t = 100fm/c
1,)1(2
V
VN N
N
ffV
dppddp )sin(,,Set of coordinates
t = 0 fm/c t = 100 fm/c
)sin( p = 260 MeV/c, Δp = 10 MeV/c,
Check of the <f> profile
Check of the fluctuation varianceon the Fermi surface
3)/30( cMeVVp
Our result: 3)/40( cMeVVcloud
In this case: ‘nucleon’ volume
Δp
Propagation of fluctuations by the unstable mean-field
Box calculations : ρ = 0.05 fm , T = 3 MeV
Fourier analysis ofthe density variance <δρδρ> :rapid growth of density fluctuations
Fragment multiplicity and charge distributions (300 nucleons)
-3
CONCLUSIONS
Study of IMF’s emitted in heavy ion collisions:
• Correlations between N/Z and velocity
• Fragments with smaller kinetic energy are more neutron rich (asy – stiff)
• Double ratios as sensitive observables to the asy-EOS
Development of a full 3D treatment of the BL theory :
•Improvement of the treatment of fluctuations in p space (thermal fluctuations)
V.Baran (NIPNE HH,Bucharest) M.Di Toro, J. Rizzo (LNS-Catania)Ph. Chomaz (GANIL, France) H.H. Wolter (Munich)
124Sn + 64Ni 35 AMeV ternary events
N/Z-IMF vs. Alignement Correlation in semi-peripheral collisions
Experiment Transp. Simulations (124/64)
Chimera data: see E.De Filippo, P.Russotto NN2006 Contr., Rio
Asystiff
Asysoft
V.Baran, Aug.06
Asystiff: more isospin migration to the neck fragments
Histogram: no selection
E.De Filippo et al. , PRC71(2005)
dppddp )sin(,,Set of coordinates
)sin( p = 260 MeV/c, Δp = 10 MeV/c,
t = 0 fm/c t = 100 fm/c
)cos(3
23
p
V
The variance of the distribution function
p = 190 MeV/c Δθ = 30°
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume: p = 190 MeV/c, θ = 20°
12.0)(2 Ff E
b=8f
mb=
10fm
ISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
BNV - transport modelb=8fmb=9 fmb=10fm
120fm/c100fm/c80fm/c
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
PII
III2R;
II
III2R
experimental data(B. Tsang et al. PRL 92 (2004) )
asysoft eos superasystiff eos
contact time
Baran, Colonna, Di Toro, Pfabe, Wolter, PRC72(2005)
Imbalance ratios
asy-soft EOS –faster equilibration
Elab = 30 Mev/A, b = 4 fm
a) softb) stiff
Competition between reaction mechanisms: fusion vs deep-inelastic
M.Colonna et al., PRC57(1998)1410
neutron-rich
proton-rich
Comparison with INDRA data
-- stiff
-- soft
forward c.m.
forward QP
I = Iin + c(Esym) (Iav – Iin)
RP = 1 – c ; RT = c - 1
softstiff
b
20% difference in the slopebetween stiff and soft
INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A: N/Z vs b
E.Galichet et al., Nucl.Phys.A submittedIPN, Orsay
if
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
PII
III2R;
II
III2R
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
PII
III2R;
II
III2R
H
LH LH
H LL
asy-soft
asy-stiff
Sn + Ni Elab = 10 MeV/Ab = 6,7,8 fm, t = 500 fm/c
More dissipative neck dynamics with asy-stiff !
64132
asy-stiff asy-soft
Octupole distribution
Competition between deep-inelastic and neck emission
V.Baran, Aug.06SPIRAL2 proposal
INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A
Isospin effects on dissipation
soft stiff
E.Galichet et al., Nucl.Phys.A submittedIPN, Orsay
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocity;
r1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot !
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124, E/A = 50 MeV/A, b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV:Freeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles: asy-stiffBlack circles: asy-soft
Asy-soft: small isospin migration
Fe: fast neutron emission
Ni: fast proton emission
Angular distributions: alignment characteristicsAngular distributions: alignment characteristics
plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the “dynamical” (gate 2) and “statistical” (gate 1) components: these last are more concentrated in the reaction plane.
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSn
Sn112
124
A
ZNR
AfZNY
12221
2
2
2ln
)(exp)(),(
not very sensitive to Esym ?
124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffT.X.Liu et al.
PRC 2004
50 AMeV
(central coll.)